Impacts of climate change on optimal mixture design of blended concrete considering carbonation and chloride ingress

Abstract

Many studies on the mixture design of fly ash and slag ternary blended concrete have been conducted. However, these previous studies did not consider the effects of climate change, such as acceleration in the deterioration of durability, on mixture design. This study presents a procedure for the optimal mixture design of ternary blended concrete considering climate change and durability. First, the costs of CO₂ emissions and material are calculated based on the concrete mixture and unit prices. Total cost is equal to the sum of material cost and CO₂ emissions cost, and is set as the objective function of the optimization. Second, strength, slump, carbonation, and chloride ingress models are used to evaluate concrete properties. The effect of different climate change scenarios on carbonation and chloride ingress is considered. A genetic algorithm is used to find the optimal mixture considering various constraints. Third, illustrative examples are shown for mixture design of ternary blended concrete. The analysis results show that for ternary blended concrete exposed to an atmospheric environment, a rich mix is necessary to meet the challenge of climate change, and for ternary blended concrete exposed to a marine environment, the impact of climate change on mixture design is marginal.

Keywords

ternary blended concrete / climate change / optimal mixture design / carbonation / chloride ingress

Introduction

Fly ash and slag are industrial by-products that are widely used as mineral admixtures in modern concrete production. Fly ash and slag present many advantages, such as reducing CO₂ emissions, lowering material costs, and improving workability and chloride ingress resistance. However, the addition of fly ash and slag to concrete reduces its carbonation resistance. To rationally use fly ash and slag while also achieving the aim of sustainability, careful examinations of their positive and negative effects should be undertaken [¹,²].

Many studies have been conducted to evaluate the sustainability of blended concrete. Celik et al. [³] found that when high volumes of fly ash and limestone are used to replace up to 55% cement, the global warming potential of concrete can be lowered. Tae et al. [⁴] reported that slag blended high-strength concrete can reduce the life cycle energy and CO₂ of a building. Rivera et al. [⁵] showed that 1 m³ concrete containing 728 kg fly ash has a strength higher than 30 MPa, higher chloride penetration resistance, and lower environmental impact. Tait and Cheung [⁶] found that by using fly ash and slag, concrete can be produced without a loss of performance while reducing the environmental impact. Yang et al. [⁷] reported that compared with Portland cement foamed concrete, alkali-activated slag foamed concrete can reduce global warming potential and photochemical oxidation potential. Wang et al. [⁸] noted that when the durability requirement of structure is satisfied, fly ash can reduce social burden and reduce cost over the long-term.

Compared with studies evaluating sustainability [³–⁸], studies about the mixture design of sustainable concrete are relatively few. Based on a genetic algorithm, neural networks, and a convex hull, Lee et al. [⁹] proposed a technique to find the optimal concrete mixture with the lowest cost. Based on neural networks and a harmony search algorithm, Lee and Yoon [¹⁰] presented a calculation procedure for mixture design of concrete considering various constraints. Kim et al. [¹¹] proposed an evolution algorithm to minimize the life cycle cost or CO₂ of concrete considering the mixing, transportation, and manufacturing stages. Based on neural networks and a genetic algorithm, Sebaaly et al. [¹²] proposed a technique to optimize aggregate gradation and binder content in asphalt mix. Tapali et al. [¹³] presented a numerical iteration method to determine concrete mixture considering strength, carbonation, and chloride durability. On the other hand, we should note that current models [⁹–¹³] have some weak points. Tapali et al. [¹³] do not consider the workability of concrete. Lee et al. [⁹], Lee and Yoon [¹⁰], Kim et al. [¹¹], and Sebaaly et al. [¹²] do not consider the constraint of concrete durability. When fly ash and slag are used to partially replace cement, the carbonation resistance of concrete will be lowered. In other words, strength alone cannot guarantee the carbonation durability of blended concrete. Moreover, these models [⁹–¹³] do not consider the impact of climate change on the mixture design of concrete. Climate change effects, such as an increasing temperature and CO₂ concentration, will accelerate the durability deterioration of concrete due to carbonation and chloride ingress. Hence, it is necessary to optimize the mixture design of fly ash and slag blended concrete considering various factors, such as climate change, durability, strength, and workability.

To overcome the weak points of current models [⁹–¹³], this study demonstrates a simple approach to determining the optimal mixture design of fly ash and slag blended concrete considering climate change, durability, strength, and workability. The total cost is set as the objective function of optimization. Based on a genetic algorithm, the optimal mixture of ternary blended concrete is determined considering various requirements, such as different climate change scenarios, carbonation durability, chloride ingress durability, and different strength levels.

Optimization design of concrete mix proportions

To optimize the mixing proportions of fly ash and slag blended ternary concrete, the objective function and constraint conditions need to be established. In this study, the objective function is set as the sum of the material cost and CO₂ emissions cost. The constraint conditions encompass the desired concrete strength, workability, component contents, component ratios, absolute volume, carbonation durability, and chloride ingress durability [¹⁴,¹⁵].

Objective Function

The objective function of optimization is written as follows:

(1)COST=COS{T}_{\mathrm{M}}+COS{T}_{{\mathrm{CO}}_2},

where COST is the cost of concrete, COS{T}_{\mathrm{M}}is the material cost of concrete, and COS{T}_{{\mathrm{CO}}_2} is the CO₂ emissions cost. For fly ash and slag blended concrete, the material cost of concrete can be calculated using the concrete components and unit price of each component as follows:

(2){COST}_{\mathrm{M}}=P{r}_{\mathrm{C}}\ast C+P{r}_{\mathrm{S}\mathrm{G}}\ast SG+P{r}_{\mathrm{F}\mathrm{A}}\ast FA+P{r}_{\mathrm{W}}\ast W+P{r}_{\mathrm{C}\mathrm{A}}*CA+P{r}_{\mathrm{S}}*S+P{r}_{\mathrm{S}\mathrm{P}}*SP,

where P{r}_{\mathrm{C}}, P{r}_{\mathrm{S}\mathrm{G}}, P{r}_{\mathrm{F}\mathrm{A}}, P{r}_{\mathrm{W}}, P{r}_{\mathrm{C}\mathrm{A}}, P{r}_{\mathrm{S}}, and P{r}_{\mathrm{S}\mathrm{P}} are unit prices of cement, slag, fly ash, water, coarse aggregate, fine aggregate, and superplasticizer, respectively. The unit prices of concrete components are shown in Table 1. C, SG, FA, W, CA, S, and SP are the masses of cement, slag, fly ash, water, coarse aggregate, fine aggregate, and superplasticizer in the concrete, respectively.

The cost of CO₂ emissions can be calculated based on the content of CO₂ emissions and the unit price of CO₂ as follows:

(3)COS{T}_{{\mathrm{CO}}_2}=P{r}_{{\mathrm{CO}}_2}\ast M_{{\mathrm{CO}}_2}=P{r}_{{\mathrm{CO}}_2}*(\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{C}}*C+\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{S}\mathrm{G}}\ast SG+\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{F}\mathrm{A}}\ast FA+\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{W}}\ast W+\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{C}\mathrm{A}}*CA+\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{S}}*S+\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{S}\mathrm{P}}*SP),

where P{r}_{{\mathrm{CO}}_2} is the unit price of CO₂, M_{{\mathrm{CO}}_2}is the content of CO₂ emission, \mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{C}}, \mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{S}\mathrm{G}}, \mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{F}\mathrm{A}}, \mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{W}},\mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{C}\mathrm{A}}, \mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{S}}, and \mathrm{C}{\mathrm{O}}_{\mathrm{2}-\mathrm{S}\mathrm{P}}are the unit CO₂ emissions of cement, slag, fly ash, water, coarse aggregate, fine aggregate, and superplasticizer, respectively [⁷]. The unit CO₂ emissions of the concrete components are shown in Table 2. The value of the unit price of CO₂ is set as 0.4817 TWD (New Taiwan dollar)/kg [¹⁵].

Constraint conditions

The objective function (the minimum value of total cost) is exposed to various constraints, for example, concrete strength, workability, component contents, component ratios, absolute volume, and durability [¹⁴].

The strength constraint means that the design strength should be higher than the required strength. The formula for the strength constraint is shown in Eq. (4) [¹⁴]:

(4)f_{\mathrm{c}}\left(t\right)\ge f_{\mathrm{cr}}\left(t\right),(t=\mathrm{3},\mathrm{7},\mathrm{28},...,\mathrm{days}),

where f_{\mathrm{c}}\left(t\right) is the concrete strength at age t and f_{\mathrm{cr}}\left(t\right) is the required strength at age t.

The workability constraint of fresh concrete is shown in Eq. (5) [¹⁴]:

(5)Slump\ge Slum{p}^{\mathrm{r}},

where {\mathit{Slump}}^{\mathrm{r}} is the needed slump of concrete.

For concrete exposed to an atmospheric environment, the carbonation durability constraint of concrete is shown in Eq. (6) [¹⁴]:

(6)x_{\mathrm{C}}\le \mathrm{C}V,

where x_{\mathrm{C}} is the carbonation depth of concrete, and CV is the cover depth of concrete.

For concrete exposed to a marine environment, the chloride ingress durability constraint of concrete is shown in Eq. (7):

(7)C{L}_{\mathrm{c}}\le C{L}_{\mathrm{th}},

where C{L}_{\mathrm{c}} is chloride content at rebar position, and C{L}_{\mathrm{th}} is the threshold value of chloride content for corrosion initiation.

The range of component contents is shown in the following:

(8)lower\le component\le upper,

where component represents the cement, fly ash, slag, water, fine aggregate, coarse aggregate, and superplasticizer. Table 3 shows the lower and upper limits of the concrete components [¹⁴].

The component ratio constraint is shown in the following:

(9)R_{\mathrm{l}}\le R_i\le R_{\mathrm{u}},

where R_i is the component ratio (for example, the water-to-binder ratio, water-to-cement ratio, and fly ash-to-binder ratio). R_{\mathrm{l}} and R_{\mathrm{u}} are the lower and upper limits of the component ratio, respectively. Table 4 shows the details of constraints of the component ratio [¹⁴].

The absolute volume constraint is shown in the following:

(10){\displaystyle \frac{W}{{\rho }_{\mathrm{W}}}}+{\displaystyle \frac{C}{{\rho }_{\mathrm{C}}}}+{\displaystyle \frac{SG}{{\rho }_{\mathrm{SG}}}}+{\displaystyle \frac{FA}{{\rho }_{\mathrm{FA}}}}+{\displaystyle \frac{S}{{\rho }_{\mathrm{S}}}}+{\displaystyle \frac{CA}{{\rho }_{\mathrm{CA}}}}+{\displaystyle \frac{SP}{{\rho }_{\mathrm{SP}}}}+V_{\mathrm{air}}=\mathrm{1},

where {\rho }_{\mathrm{W}}, {\rho }_{\mathrm{C}}, {\rho }_{\mathrm{SG}}, {\rho }_{\mathrm{FA}}, {\rho }_{\mathrm{S}}, {\rho }_{\mathrm{CA}}, and {\rho }_{\mathrm{SP}} are the densities of water, cement, slag, fly ash, sand, coarse aggregate, and superplasticizer, respectively, and V_{\mathrm{air}} is the volume of air in concrete. The densities of water, cement, slag, fly ash, sand, coarse aggregate, and superplasticizer are 1000, 3150, 2850, 2220, 2660, 2540, and 1220 kg/m³, respectively. Equation (10) implies that the sum of each concrete component should equal 1 m³ [¹⁴].

Property evaluation of the fly ash and slag blended concrete

Strength model and slump model

Yeh [¹⁴] conducted experimental studies on the strength and slump of fly ash and slag blended concrete. The 28-day compressive strength of concrete in Yeh’s study [¹⁴] ranged from 25 to 50 MPa, and the slump of concrete ranged from 5 to 25 cm. The water-to-binder ratio ranged from 0.3 to 0.7. The upper and lower limits of the content of concrete components are shown in Table 3. The upper and lower limits of the ratio of concrete components are shown in Table 4.

Based on the experimental results of the compressive strength [¹⁴], the 28-day compressive strength of fly ash and slag ternary blended concrete is evaluated using equivalent water-to-binder ratios (Abram’s law) as follows:

(11)f_{\mathrm{c}}={\displaystyle \frac{\mathrm{112.02}}{{\mathrm{7.76}}^{\frac{W}{C+\mathrm{0.30}FA+\mathrm{0.91}SG}}}},

where f_{\mathrm{c}} is compressive strength (MPa), and 0.30 and 0.91 are strength efficiency factors of fly ash and slag respectively. The strength efficiency factor of slag is higher than that of fly ash.

Based on the experimental results of the slump [¹⁴], the slump of ternary blended concrete is evaluated used a linear equation. The variables of this linear equation are water content, water-to-binder ratio, fly ash-to-binder ratio, slag-to-binder ratio, superplasticizer content, and sand ratio. The regression equation of slump is shown as follows:

(12)Slump=\mathrm{0.369}W-\mathrm{40.02}{\displaystyle \frac{W}{FA+SG+C}}+\mathrm{15.32}{\displaystyle \frac{FA}{FA+SG+C}}+\mathrm{22.61}{\displaystyle \frac{SG}{FA+SG+C}}+\mathrm{0.85}*SP-\mathrm{34.68}{\displaystyle \frac{S}{S+CA}}-\mathrm{37.96},

where the unit of slump is cm. This equation shows that concrete slump increases with increasing water content, fly ash-to-binder ratio, slag-to-binder ratio, and superplasticizer content, and decreases with increasing sand ratio.

The prediction results of strength and slump are shown in Figs. 1(a) and 1(b), respectively. The relative coefficients between prediction results and experimental results of strength and slump are 0.985 and 0.902, respectively.

Carbonation model

Papadakis and Tsimas [¹⁶,¹⁷] proposed a general equation for evaluating the carbonation depth of concrete containing fly ash and slag. The equation considers both concrete material properties and environmental exposure conditions. When the ambient relative humidity is higher than 50%, the carbonation depth of fly ash and slag blended concrete can be determined as follows [¹,¹⁶,¹⁷]:

(13)x_{\mathrm{c}}^{}=\sqrt{{\displaystyle \frac{\mathrm{2}{D}_{{\mathrm{CO}}_2\mathrm{-ref}}{\left[{\mathrm{CO}}_{\mathrm{2}}\right]}_{0}t}{\mathrm{0.218}*(C+\mathrm{0.7}*SG+\mathrm{0.5}*FA)*{\alpha }_{\mathrm{H}}}}},

D_{{\mathrm{CO}}_2\mathrm{-ref}}=\mathrm{6.1}*{\mathrm{10}}^{-\mathrm{6}}

{\left({\displaystyle \frac{\left[W-\mathrm{0.267}*(C+\mathrm{0.7}*SG+\mathrm{0.5}*FA)*{\alpha }_{\mathrm{H}}\right]/\mathrm{1000}}{{\displaystyle \frac{C+\mathrm{0.7}*SG+\mathrm{0.5}*FA}{{\rho }_{\mathrm{c}}}}+{\displaystyle \frac{W}{{\rho }_{\mathrm{w}}}}}}\right)}^{\mathrm{3}}

(14){\left(\mathrm{1}-{\displaystyle \frac{RH}{\mathrm{100}}}\right)}^{\mathrm{2.2}},

where x_{\mathrm{c}}^{} is the carbonation depth of concrete, D_{{\mathrm{CO}}_2\mathrm{-ref}} is CO₂ diffusivity at a reference temperature of 20°C, {\left[{\mathrm{CO}}_{\mathrm{2}}\right]}_0 is the CO₂ concentration at concrete surface, {\alpha }_{\mathrm{H}}is the degree of reaction of binders ({\alpha }_H=\mathrm{1}-\exp (-\mathrm{3.38}*W/(C+\mathrm{0.7}*SG+\mathrm{0.5}*FA)) [¹,²], and RH is environmental relative humidity. The carbonation efficiency factors of slag and fly ash are 0.7 and 0.5, respectively [¹⁷]. In the denominator of Eq. (13), \mathrm{0.218}*(C+\mathrm{0.7}*SG+\mathrm{0.5}*FA)*{\alpha }_{\mathrm{H}} refers to the content of carbonatable substances in concrete. In the numerator of Eq. (14), \left[W-\mathrm{0.267}*(C+\mathrm{0.7}*SG+\mathrm{0.5}*FA)*{\alpha }_{\mathrm{H}}\right]/\mathrm{1000} is the porosity of carbonated concrete. Figures 2(a)–2(c) shows parameter analysis about effects of mineral admixtures on carbonation depth (the binder content is assumed as 300 kg/m³, CO₂ concentration is assumed as 0.04%, temperature is assumed as 20°C, and relative humidity is assumed as 0.65). As the increasing of replacement ratios of mineral admixtures, the carbonation depth of concrete increases (Figs. 2(a)–2(b)). As the decreasing of water to binder ratios, the carbonation depth of concrete decreases (Figs. 2(b)–2(c)). Given a certain replacement ratio, the sequence of carbonation depth is fly ash blended concrete>fly ash plus slag blended concrete>slag blended concrete>control concrete. This sequence agrees with results from experimental studies [¹⁶,¹⁷].

The effect of environmental temperature on CO₂ diffusivity can be viewed using the Arrhenius law as follows [¹⁷]:

(15)D_{{\mathrm{CO}}_2}\left(T\right)=D_{{\mathrm{CO}}_2\mathrm{-ref}}\exp \left[{\beta }_{{\mathrm{CO}}_2}({\displaystyle \frac{\mathrm{1}}{T_{\mathrm{ref}}}}-{\displaystyle \frac{\mathrm{1}}{T}})\right],

where D_{{\mathrm{CO}}_2}\left(T\right) is CO₂ diffusivity at a temperature T, and {\beta }_{{\mathrm{CO}}_2} is the activation energy of diffusion CO₂ ({\beta }_{{\mathrm{CO}}_2}= 4690). For climate change conditions, CO₂ concentration and CO₂ diffusivity are dependent on exposure time. The time-averaged CO₂ concentration {\displaystyle \frac{{\displaystyle {\int }_{\mathrm{0}}^t{\left[{\mathrm{CO}}_2\right]}_t}\mathrm{d}t}{t}} and CO₂ diffusivity {\displaystyle \frac{{\displaystyle {\int }_{\mathrm{0}}^t{\left[D_{{\mathrm{CO}}_2}\right]}_t}\mathrm{d}t}{t}} are used for climate change conditions.

Chloride ingress model

Assuming diffusion is the main mechanism of chloride ingress, the chloride content in concrete can be determined based on Fick’s second law as follows [¹⁸,¹⁹]:

(16)C_{\mathrm{CL}}(x,t)=C_{\mathrm{s}}[\mathrm{1}-\mathrm{erf}({\displaystyle \frac{x}{\mathrm{2}\sqrt{D_{\mathrm{m}}t}}}\left)\right],

where C_{\mathrm{CL}} is chloride content at the distance x, C_{\mathrm{s}} is chloride content at the surface of concrete, \mathrm{erf} is the error function, D_{\mathrm{m}} is the time-averaged diffusion coefficient. D_{\mathrm{m}} can be calculated as follows [¹⁸,¹⁹]:

(17)

(18)D_m=D_{\mathrm{ref}}[\mathrm{1}+\frac{t_R}{t}{\displaystyle \frac{m}{\mathrm{1}-m}}]{\left({\displaystyle \frac{t_{\mathrm{ref}}}{t_R}}\right)}^m,t\ge t_{\mathrm{R}},

where D_{\mathrm{ref}} is the chloride diffusion coefficient at reference time t_{\mathrm{ref}} (t_{\mathrm{ref}} = 28 days), t_{\mathrm{R}}is the time when chloride diffusion coefficient is assumed to be constant (t_{\mathrm{R}} = 30 years) [¹⁸], and m is the diffusion decay index. D_{\mathrm{ref}} can be determined as follows [¹⁹]:

(19)D_{\mathrm{ref}}=\mathrm{10}{(}^{-\mathrm{12.06}+\mathrm{2.4}}{}^{W/B}),

where W/B is the water-to-binder ratio. As shown in Eq. (19), D_{\mathrm{ref}}decreases with increasing water-to-binder ratio.

The diffusion decay index m can be determined as follows [¹⁹]:

(20)m=\mathrm{0.2}+\mathrm{0.4}(\mathrm{\%}FA/\mathrm{50}+\mathrm{\%}SG/\mathrm{70}),

where %FA and %SG are the replacement levels of fly ash and slag in concrete mixtures, respectively. As shown in Eq. (20), with increasing replacement levels of fly ash and slag, the diffusion decay index also increases. This is because of further hydration of mineral admixtures and improvement of chloride binding capacity during the exposure period. The value of m should be less than 0.6.

Figures 2(d)–2(f) shows parameter analysis about effects of mineral admixtures on chloride ingress (surface chloride content is assumed as 2.95 kg/m³, and temperature is assumed as 20°C). As the increasing of replacement ratios of mineral admixtures, the chloride content at cover depth (40 mm) decreases (from Figs. 2(d)–2(e)). As the decreasing of water to binder ratios, the chloride content at cover depth (40 mm) decreases (from Figs. 2(e)–2(f)). Given a certain replacement ratio, the sequence of chloride content is control concrete>slag blended concrete>fly ash plus slag blended concrete>fly ash blended concrete.

The dependence of chloride diffusivity on temperature can be described by using the Arrhenius law as follows [¹⁸,¹⁹]:

(21)D_{\mathrm{cl}}\left(T\right)=D_m\exp \left[{\beta }_{\mathrm{cl}}\left({\displaystyle \frac{\mathrm{1}}{T_{\mathrm{ref}}}}-{\displaystyle \frac{\mathrm{1}}{T}}\right)\right],

where {\beta }_{\mathrm{cl}}(1/K) is the activity energy of chloride diffusion ({\beta }_{\mathrm{cl}} = 4210 [¹⁸,¹⁹]). For climate change conditions, due to increasing temperature, chloride diffusivity will increase. In this study, the average temperature over the time period is used to consider the global warming effect. The time-averaged chloride diffusivity {\displaystyle \frac{{\displaystyle {\int }_{\mathrm{0}}^t{\left[D_{\mathrm{cl}}\right]}_t}\mathrm{d}t}{t}} is used for considering climate change.

Summary of optimization design approach

A flowchart of optimization design is shown in Fig. 3. First, the objective function was set as the total cost of concrete, which equals the sum of the material cost and CO₂ emissions cost. Secondly, the property evaluation models, namely, the compressive strength, slump, carbonation, and chloride ingress models, were proposed. In particular, the carbonation and chloride ingress models considered the acceleration of durability deterioration due to climate change. Thirdly, constraint conditions were proposed. These constraints included service life, upper and lower limit of concrete components, mass ratio of concrete components, and absolute volume of concrete. Furthermore, based on an optimization algorithm, optimized concrete mixtures that meet various performance requirements could be acquired.

The technique used for solving the objective function with constraints is the genetic algorithm [²⁰,²¹]. The genetic algorithm (GA) originates from computer simulation of biological systems. The basic steps of a basic genetic algorithm are: 1) generate random population; 2) determine the fitness of the individual and make selection according to fitness; 3) generate new individuals based on crossover and mutation operations; 4) check termination criteria. If termination criteria are not satisfied, return to step 2).

In this study, we used the MATLAB Global Optimization Toolbox for solving objective optimization with constraints [²⁰]. The objective function and constraints equation can be set in the MATLAB Global Optimization Toolbox and, according to the genetic algorithm, the optimal mixture with minimum cost and meeting various constraints can be found.

Illustrative examples for concrete exposed to an atmospheric environment

In this section, we show an illustrative example of the mixture design of fly ash and slag blended concrete exposed to an atmospheric environment with different climate change scenarios. According to the concrete design code [²²], to reach a 50-year service life, for corrosion induced by carbonation at moderate humidity, the required 28-day compressive strength is 30 MPa, and the required cover depth is 25 mm. To highlight the effect of climate change on service life and concrete mixture design, the climate change scenarios proposed by the Intergovernmental Panel on Climate Change (IPCC) are used. The increases of CO₂ concentration and temperature for different climate change scenarios are shown in Fig. 4. Three climate change scenarios are considered, i.e., no climate change, representative concentration pathway (RCP) 4.5, and RCP 8.5 [²³]. RCP 8.5 shows higher increases of CO₂ concentration and temperature than RCP 4.5. In this study, the starting year of exposure is assumed to be 2000, starting exposure temperature is assumed to be 20°C, and relative humidity is assumed to be 0.65. The requirement slump is assumed to be 6.5 cm. The air content in concrete mixtures (V_air) was assumed to be 2%. In addition, Fig. 4 shows climate changes in a 200-year span. While in our analysis, we only use climate changes from the year 2000 to the year 2050 because the required service life of concrete is assumed as 50 years.

Proportional design without considering carbonation

When fly ash and slag are used to partially replace cement, the carbonation resistance of concrete is impaired. To highlight the importance of carbonation durability, in Section 3.1 we make a mixture design of fly ash and slag blended concrete without considering carbonation. Based on the genetic algorithm considering various constraints, the mixture for concrete with a 30 MPa strength is calculated and shown in Table 5. This mixture is named Mix 1. The performance of Mix1 is shown in Table 6. The mass ratio of components of Mix 1 is shown in Table 7. The strength and slump of Mix 1 can meet the requirements of the mixture design. The range of concrete components and mass ratios of concrete components can meet the constraints shown in Tables 3 and 4. In addition, the superplasticizer-to-binder ratio of Mix 1 is equal to the lower limit of the superplasticizer-to-binder ratio (shown in Table 4). This is because the price of superplasticizer is much higher than other components of concrete. The sand ratio of Mix 1 is also equal to the lower limit of the sand ratio (shown in Table 4). This is because the price of sand is higher than coarse aggregate (shown in Table 1).

By using the carbonation model shown in Section 2.3.2, we can calculate the carbonation depth of Mix 1. The results of carbonation depth of Mix 1 for the no climate change scenario are shown in Fig. 5. It is shown that after a 50-year service life, the carbonation depth of Mix 1 is much higher than the cover depth. Hence, Mix 1 cannot meet the requirements of carbonation durability. In other words, for fly ash and slag blended concrete, strength alone cannot guarantee carbonation durability, and it is necessary to consider the constraint of carbonation durability for blended concrete exposed to an atmospheric environment.

Proportional design considering carbonation

Section 3.1 shows the necessity of considering carbonation durability of blended concrete. In this section, we make a mixture design of blended concrete considering carbonation durability with various climate change scenarios.

Based on the genetic algorithm, the mixture for no climate change scenario is calculated. The mixture for no climate change scenario is named Mix 2. The concrete mixture, performance of concrete, and mass ratio of components of Mix 2 are shown in Tables 5, 6, and 7, respectively. Based on the carbonation model, the carbonation depths of Mix 2 for various climate change scenarios are calculated and shown in Figs. 6(a) to 6(c). For the no climate change scenario, after a 50-year service life, the carbonation depth of Mix 2 is equal to the cover depth (Fig. 6(a)). For RCP 4.5 and RCP 8.5 climate change scenarios, after a 50-year service life, the carbonation depth of Mix 2 is higher than the cover depth (Figs. 6(b) and 6(c)). This means that Mix 2 can meet the requirements of carbonation durability for the no climate change scenario, but cannot meet the requirements for RCP 4.5 and RCP 8.5 climate change scenarios. This is because the CO₂ concentration and temperature of RCP 4.5 and RCP 8.5 are much higher than in the no climate change scenario.

Similarly, by using the genetic algorithm, the mixture for the RCP 4.5 scenario is calculated. The mixture for RCP 4.5 scenario is named Mix 3. Based on the carbonation model, the carbonation depths of Mix 3 for the RCP 4.5 and RCP 8.5 scenarios are calculated and shown in Fig. 7. Figure 7(a) shows that Mix 3 can meet the requirements of carbonation durability for the RCP 4.5 scenario. However, Mix 3 cannot meet the requirements for the RCP 8.5 climate change scenario (Fig. 7(b)). This is because the CO₂ concentration and temperature of the RCP 8.5 scenario is much higher than in the RCP 4.5 climate change scenario. In addition, for carbonation depth, compared to the case of no climate change, the difference between RCP8.5 and RCP4.5 (Figs. 6(b) and 6(c), Figs. 7(a) and 7(b)) seems not significant, despite existing. Probably it is because, in the span of year 2000–2050, CO₂ and temperature rise difference between RCP 8.5 and RCP 4.5 are not big.

Finally, by using the genetic algorithm, the mixture for the RCP 8.5 scenario is calculated. The mixture for the RCP 8.5 scenario is named Mix 4. Based on the carbonation model, the carbonation depth of Mix 4 is calculated and shown in Fig. 8. This figure shows that Mix 4 can meet the requirements of carbonation durability for the RCP 8.5 scenario. After a 50-year service life, the carbonation depth of Mix 4 is equal to the cover depth.

As shown in Table 6, the strengths of Mix 2 (no climate change scenario), Mix 3 (RCP 4.5 scenario), and Mix 4 (RCP 8.5 scenario) are 36.14, 38.73, and 39.56 MPa, respectively. The strengths of Mix 2–Mix 4 are much higher than the requirement design strength 30 MPa (Mix 1). Hence for fly ash and slag blended concrete, carbonation durability is the control factor for mixture design. In particular, from the no climate change scenario to the RCP 8.5 scenario, the increase of CO₂ concentration and temperature becomes obvious, carbonation of concrete is accelerated, and the requirement strength corresponding to each scenario increases (shown in Fig. 9).

Illustrative examples for concrete exposed to a marine environment

This section shows mixture design of concrete exposed to a marine environment combined with various climate change scenarios. According to the concrete design code [²²], to reach a 50-year service life, for corrosion induced by chloride ingress, the required 28-day compressive strength is 32 MPa, and the required cover depth is 40mm. The increases of temperature for different climate change scenarios (no climate change, RCP 4.5, and RCP 8.5) are shown in Fig. 4(b). In this study, the starting year of exposure is assumed to be 2000, at which point the temperature is assumed to be 20°C. The requirement slump is assumed to be 6.5 cm. The air content in concrete mixtures (V_air) is assumed to be 2%. The surface chloride content is assumed to be 2.95 kg/m³, and the chloride threshold is assumed to be 1.2 kg/m³ [¹⁸,¹⁹].

When fly ash and slag are used to partially replace cement, the chloride ingress resistance of concrete is enhanced. In this section, first, we make a mixture design of fly ash and slag blended concrete without considering chloride ingress. Based on the genetic algorithm considering various constraints, the mixture for 32 MPa strength is found and shown in Table 5. This mixture is named Mix 5. The performance and mass ratio of components of Mix 5 are shown in Tables 6 and 7, respectively. The strength and slump of Mix 5 can meet the requirements of the mixture design. The range of the concrete components and mass ratios of the concrete components can meet the constraints shown in Tables 3 and 4. In addition, we find that the water contents of Mix 1 to Mix 5 are very similar. This is because for different mixtures, the water-to-solid ratios are equal to the lower limit of water-to-solid ratios of 0.08 (as shown in Table 4).

Based on the chloride ingress model, the chloride content at cover depth of Mix 5 is calculated and shown in Fig. 10. First, after a 50-year exposure, for different climate change scenarios, the chloride contents at cover depth are still lower than the chloride threshold value (1.2 kg/m³). This means that the constraint from chloride ingress can be satisfied. Secondly, from the no climate change scenario to the RCP 8.5 climate change scenario, chloride content increases. However, compared with carbonation depth shown in Fig. 6, the increment of chloride content shown in Fig. 10 is not obvious. This is because for concrete carbonation, both CO₂ concentration increase and temperature increase will contribute to the increase of carbonation, while for chloride ingress, only temperature increase contributes to the increase of chloride penetration.

Summarily, when the strength of blended concrete and plain concrete is the same, the chloride ingress resistance of blended concrete is much higher than that of plain concrete. Although chloride ingress is accelerated due to climate change, after a 50-year service life, chloride content at cover depth is still lower than the chloride threshold for corrosion initiation. In other words, climate change has no impact on optimization design of blended concrete exposure to a chloride ingress environment.

The CO₂ cost, material cost, and total cost of Mix 1–Mix 5 are shown in Fig. 11. It is shown that as the strength of concrete increases, the CO₂ cost, material cost, and total cost also increase.

Discussions

The specific contributions of this study are summarized as follows: first, previous studies [⁹–¹³] about sustainable concrete mainly focused on concrete strength and CO₂ emissions, but omitted the effect of climate change on durability. Contrastively, this study considers concrete durability coupled with various climate change scenarios, concrete strength, CO₂ emissions, materials cost, and concrete slump. The optimization results of this study can directly reflect the impact of climate change on mixture design. Hence this study fills the gaps in previous studies [⁹–¹³]. Second, carbonation and chloride ingress are among major durability issues for reinforced concrete structures. This study proposes an integrated model considering both carbonation durability of atmospheric concrete and chloride ingress of marine concrete. The proposed model is useful for material design of concrete with various exposure environments. Third, the proposed integrated model is valid for multiple types of concrete, such as ternary blended concrete, binary blended concrete, and plain concrete. The proposed model can design sustainable concrete containing different supplementary cementitious materials.

The aim of this study was to propose a general methodology for the optimization of concrete mixtures for various countries and exposure conditions. The proposed method in this study can be regarded as a general method for the design of low-cost and low-CO₂ blended concrete considering climate change and durability. For different countries, the compressive strength models [¹⁷,²⁴], slump models [²⁵,²⁶], carbonation models [²⁷,²⁸], chloride ingress models [²⁹,³⁰], and climate change scenarios [²⁹] may be different from the equations proposed. Other researchers can use their own models to replace the relevant equations shown this study and, furthermore, select the objective function and make their own optimizations by using the GA. Although other researchers’ equations may be different from those used in this study, the design procedure is very similar.

Conclusions

This study presented a procedure for the optimal design of fly ash and slag blended concrete considering climate change and durability.

First, the cost of CO₂ emissions and cost of materials were calculated based on the concrete mixture and unit prices. The total cost was equal to the sum of the material cost and the CO₂ emissions cost, and was set as the objective function of optimization.

Second, property evolution models, namely, strength, slump, carbonation, and chloride ingress models were proposed. The carbonation and chloride ingress models considered the acceleration of durability deterioration due to climate change. Constraints of the optimization included strength, slump, service life, upper and lower limit of concrete components, mass ratio of concrete components, and absolute volume.

Third, a genetic algorithm was used to find the optimal mixture considering various constraints. Illustrative examples were shown for designing ternary blended concrete. The analysis results showed that: 1) for ternary blended concrete exposed to an atmospheric environment, to meet the challenge of climate change, a rich mix is necessary; 2) for ternary blended concrete exposed to a marine environment, the impact of climate change on mixture design is marginal.

Summarily, this study combines a genetic algorithm with durability models considering climate change. The optimization results of this study can directly reflect the impact of climate change on mixture design. The proposed model is useful for material design of concrete with various exposure environments and different supplementary cementitious materials. The proposed method in this study can be regarded as a general method for the design of low-cost and low-CO₂ blended concrete considering climate change and durability. Other researchers can use their own models to replace the relevant equations shown in this study. Although the equations may be different, the design procedure is very similar.

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